The problem posed in this paper is to give a relation connecting the noise stability of a communication system in which error-correcting codes are used to the parameters of these codes. The amountxof code combinations is found, which differ from each other by not less than a given number of elements for a given arrangement of all the possible combinations. It is proved that the quantity...
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Consider a list ofbwords, each word being a string of letters from a given fixed alphabet ofaletters. If every string of words drawn from this list, when written out in letters without additional space marks to separate the words, is uniquely decipherable, then begin{equation} a^{-l_1} + a^{-l_2} + cdots + a^{-l_b} leq 1, qquad qquad (1) end{equation} wherel_i, 1 leq i l...
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This note discusses the problem of maximizing the rate of flow from one terminal to another, through a network which consists of a number of branches, each of which has a limited capacity. The main result is a theorem: The maximum possible flow from left to right through a network is equal to the minimum value among all simple cut-sets. This theorem is applied to solve a more general problem, in w...
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The spectrum of the output of a half-wave rectifier is derived for an input which is the sum of random noise and two sinusoidal signals of different frequencies. The method used is the characteristic function method described by Rice. The components of the output spectrum are given as infinite series of hypergeometric functions. If both the input signals .are small compared with the noise, it is s...
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Solutions are obtained in open form for the optimum, probability-computing detector of either Gaussian signals, or known signals transmitted via scatter-paths, where the signals have been further perturbed by additive white Gaussian noise. The optimum receiver operates on the received waveforms with filter-functions and biasing constants determined by pairs of inhomogeneous and homogeneous integra...
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A coincidence method of detecting signal in the presence of noise is compared to the statistically optimum Neyman-Pearson procedure utilizing signal integration and threshold detection. In this coincidence procedure a specified number of the fixed group of successive pulses are required to exceed a voltage threshold level. The analysis is carried out for the case of constant-amplitude signals only...
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The sampling theorem is recognized as an interpolation formula. Starting from the Lagrange Polynomial, this theorem is developed under conditions which are of broader applicability than those usually stated. Such a view point indicates the essential unity of temporal and frequency domain application. It will also be shown that the theorem is applicable as an exact interpolation formula throughout ...
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For an arbitrary random processxi(t)there exists a functionx(t)which may be obtained by infinite clipping. The axis crossings ofx(t)are identical with those ofxi(t). This paper relates the probability densityP(tau)of axis-crossing intervals togamma(tau), the autocorrelation function ofx(t), i.e., the autocorrelation after...
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A set of black-and-white patterns can be identified by successive sampling of the individual "cells" which constitute these patterns. If the number of patterns isPand the number of cells isC, it is possible to find, for any specified sampling sequence at leastC - P + 1cells which may be omitted without obstructing unique identification. Such redundant cells can be ...
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